The Ivory Coast forward had been heavily linked with a move to Merseyside and has now followed former Latics' boss Roberto Martinez to Goodison Park.
Wigan chairman Dave Whelan said last week that he expected the 29-year-old to leave after Everton met the £5m buy-out clause in Kone's contract.
And although there was also reported interest from Newcastle, Kone has opted to be re-united with his former boss who left Wigan for Everton following David Moyes' appointment as Manchester United manager.
Martinez originally signed Kone from Spanish side Levante in 2012 and the former PSV Eindhoven man scored 11 goals last season, although he was unable to prevent Wigan being relegated from the Premier League.
Kone has been on international duty and is currently on holiday but he will join up with his new club later this month ahead of the new Premier League campaign.
"I feel delighted," said Kone. "I'm really happy about joining this team.
"For me it is the fruition of work that has been going on for a month now. I'm really pleased to be here and I hope that everything goes well and I can have a great season for the club, just like I did last year with Wigan.
"For me it's an honour to be back working with the manager once again.
"Last season he really helped me a lot. For my first season I did the absolute best I could but I think that joining up with him at this club is like another dimension for me, and I hope that I'm going to continue to improve alongside him.
"I think that with the quality of squad Everton has, we will have a good season, and I hope to score as many goals as I can next season."
The forward feels his career is moving up a level and is backing himself to deliver for the Goodison Park club.
"Every player dreams of playing for a bigger club and coming here is a big step up for me," he said.
"I hope to be able to fulfil all my dreams and get as far as I can through hard work.
"I really believe in this team and I think we will have a great campaign next season. I can't wait to make my debut for this club.
"I'm raring to go because, when you join a club, it's that desire to start working that first comes to mind.
"I'm ready and willing to get started and can't wait to meet up with my team-mates and the coaching staff."